1. Field of the Invention
The present invention relates to guidance and control systems, and more particularly, to adaptive guidance and control systems.
2. Background Information
When guiding a device, such as an interceptor missile, toward a moveable object or target, it is known to address target maneuvering in the control of the missile. For example, the object may be configured to induce a miss distance by initiating an acceleration maneuver. Against a missile utilizing a proportional guidance system, target maneuvering can be controlled as a function of any known missile parameters, such as the missile's autopilot time constant (its agility) and effective navigation ratio. If the target does not have a priori knowledge of the missile parameters, does not know time to intercept, and/or does not have visual or electronic contact with the missile, then periodic maneuver sequences such as a barrel roll or weave maneuver can be executed. In addition to calculated maneuvering, targets such as tactical ballistic missiles (TBM) can unintentionally spiral or weave into resonance as they re-enter the atmosphere due to either mass or configuration asymmetries.
The control of a moving object to a maneuverable target is discussed in the book, “Tactical and Strategic Missile Guidance”, Third Edition, Volume 176, by Zarchan, and in a Zarchan article, “Proportional Navigation and Weaving targets”, Journal of Guidance, Control, and Dynamics, Volume 18, No. 5, September-October 1995, pages 969-974, both of which are incorporated herein by reference. Zarchan discloses a scalar classical pro nav guidance law as:                               n          c                =                                            N              l                        ⁢                          V              c                        ⁢                          λ              .                                =                                                                                          N                    l                                    ⁡                                      (                                          y                      +                                                                        y                          .                                                ⁡                                                  (                                                      t                            go                                                    )                                                                                      )                                                                    t                  go                  2                                            ⁢                                                           ⁢              where              ⁢                                                           ⁢              λ                        =                          (                              y                                  R                  TM                                            )                                                          (        1        )            wherein the missile acceleration command (nc) is perpendicular to the target line-of-sight vector for small line-of-sight angles (λ) as evidenced by the λ=(y/RTM) approximation. Small angle approximations are used to simplify modern guidance laws that use scalar Y axis Cartesian Kalman filter estimates of target-to-missile range and velocity (y and {dot over (y)}). For a dual-range air-to-air missile, however, guidance laws with these small line-of-sight angle approximations result in excessive missile divert requirements, which waste valuable on-board energy, and can degrade performance.
“Line of Sight Reconstruction for Faster Homing Guidance”, presented as Paper 83-2170 at the AIAA Guidance and Control Conference, Gatlinburg, Tenn., Aug. 15-17, 1983; received Aug. 24, 1983: revision received Jan. 3, 1984. Copyright® 1983, by F. W. Nesline and P. Zarchan, which is incorporated herein by reference, describes line-of-sight ( LOS) reconstruction. This Zarchan document discloses another scalar pro nav guidance law as:                               n          c                =                                                            N                l                            ⁡                              (                                  y                  +                                                            y                      .                                        ⁡                                          (                                              t                        go                                            )                                                        +                                      ZEM                    TM                                                  )                                                    t              go              2                                -                                    C              4                        ⁢                          n              L                                                          (        2        )                                          where          ⁢                                           ⁢                      ZEM            TM                          =                  0.5          ⁢                                           ⁢                      t            go            2                    ⁢                      n            T                                              (        3        )            
The missile acceleration command (nc) is over amplified by N′ and negated by an achieved missile acceleration quantity (C4 nL) to make-up for expected dynamics lag in the missile's autopilot. Zarchan also describes a weaving target guidance law with a priori estimates of the target weaving frequency. Equation (2) uses an estimated target acceleration (nT) presented in Equation (3) as the zero effort miss (ZEMTM) due to a target maneuver.
Zero effort miss is defined as the distance the missile would miss if the target continued along its present trajectory and there were no more missile acceleration commands. A condition of Equation (3) is that the zero effort miss is caused by constant target acceleration for all time-to-go before intercept. Zarchan derives the zero effort miss due to a target maneuver frequency (ωT) with target acceleration and acceleration rate magnitudes (nT and {dot over (n)}T), and documents the scalar weaving target guidance law as:                               ZEM          TM                =                                            (                                                1                  -                                      cos                    ⁢                                                                                   ⁢                                          ω                      M                                        ⁢                                          t                      go                                                                                        ω                  T                  2                                            )                        ⁢                          n              T                                +                                    (                                                                                          ω                      M                                        ⁢                                          t                      go                                                        -                                      sin                    ⁢                                                                                   ⁢                                          ω                      M                                        ⁢                                          t                      go                                                                                        ω                  M                  3                                            )                        ⁢                                          n                .                            T                                                          (        4        )            
However, known systems do not address how to estimate a target maneuver frequency (ωT) for the weaving target guidance law, and use small angle approximations.
U.S. Pat. No. 4,494,202 (Yueh), the disclosure of which is hereby incorporated by reference, describes a fourth order predictive augmented proportional navigation system terminal guidance design with missile attached target decoupling. In Yueh's system, the estimated value of target lateral displacement is derived from a representation of the measured LOS angle combined with radome error and noise in the system, and small angle approximations are used. The gain C3 associated with a predetermined estimate of target maneuver augments the target acceleration term into a proportional navigation design. However, this gain is not adaptive, and relies on the target bandwidth (i.e., a predetermined value based on expected target maneuver). Thus, Yueh discloses an angular guidance approach which allows guidance for all line-of-sight (LOS) angles, yet maintains the conventional use of small angle approximation. Yueh does not support the framework for building a fully descriptive target state equation for adaptively estimating a target maneuver frequency in Cartesian space.
Warren, Price, Gelb and Vander Velder in “Direct Statistical Evaluation of Nonlinear guidance systems” AIAA Paper No. 73-836, which is incorporated herein by reference, disclose several missile guidance laws. In particular two optimal linear guidance laws C and D are shown that use Kalman filters which are synonymous with the classical optimal guidance control laws of Zarchan. Guidance law C minimizes the performance index, neglecting autopilot dynamics, resulting in C4=0 and C3 is a function of the target bandwidth, λt. Guidance law D is derived including the first-order autopilot model dynamics and the resulting n′ and C4 are both functions of λm and tgo. The gains and navigation ratios for the Classical optimal guidance control laws of Warren et al., and Yueh are shown in Table 1.
TABLE 1C3C4n′ (γ = 0)Law C            ⅇ              -                  X          T                      +          X      T        -    1        X    T    2  03Law D            ⅇ              -                  X          M                      +          X      M        -    1        X    M    2        6    ⁢                   ⁢          X      M      2        ⁢                   ⁢          (                        ⅇ                      -                          X              M                                      +                  X          M                -        1            )                                                2            ⁢                                                   ⁢                          X              M              3                                +          3          +                      6            ⁢                                                   ⁢                          X              M              2                                -                                                          12            ⁢                                                   ⁢                          X              M                        ⁢                          ⅇ                              -                                  X                  M                                                              -                      3            ⁢                                                   ⁢                          ⅇ                                                -                  2                                ⁢                                  X                  M                                                                        where: XT = λT {circumflex over (t)}go, XM = λM{circumflex over (t)}go; {circumflex over (t)}go = Estimated Time-to-Go [sec]λT = Target Maneuver Bandwidth [rad/sec]λM = Missile Autopilot/Airframe Bandwidth [rad/sec]γ = Optimal quadratic Cost Function Weighting Factor 
As with the systems disclosed by Zarchan, Yueh's system and those disclosed in Warren, are subject to the classical augmented proportional navigation problem, the zero or constant maneuver frequency assumptions, thus wasting valuable energy against highly maneuverable targets.